摘要：If the deforming matter is to be in thermodynamic equilibrium, then all constitutive theories, includingthose for heat vector, must satisfy conservation and balance laws. It is well known that only the second lawof thermodynamics provides possible conditions or mechanisms for deriving constitutive theories, but theconstitutive theories so derived also must not violate other conservation and balance laws. In the work presentedhere constitutive theories for heat vector in Lagrangian description are derived (i) strictly using theconditions resulting from the entropy inequality and (ii) using theory of generators and invariants in conjunctionwith the conditions resulting from the entropy inequality. Both theories are used in the energy equationto construct a mathematical model in R1 that is utilized to present numerical studies using p-version leastsquares finite element method based on residual functional in which the local approximations are consideredin higher order scalar product spaces that permit higher order global differentiability approximations.The constitutive theory for heat vector resulting from the theory of generators and invariants contains up tocubic powers of temperature gradients and is based on integrity, hence complete. The constitutive theoryin approach (i) is linear in temperature gradient, standard Fourier heat conduction law, and shown to besubset of the constitutive theory for heat vector resulting from the theory of generators and invariants.
关键词：Nonlinear Heat Conduction; Solid Continua; Lagrangian Description; Generators and Invariants;Entropy Inequality; Integrity; Temperature Gradient
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